Initialization-Free Distributed Network Size Estimation Via Implicit-Explicit Discretization Method

Abstract

This paper proposes a distributed algorithm for estimating the network size, which is the total number of agents in a network. Our approach is based on an optimization problem, where the solution corresponds to the network size and the objective function can be decomposed into individual agents' objectives. This enables the use of distributed methods such as the primal-dual gradient method. We focus on a continuous-time primal-dual gradient method and adapt it using an implicit-explicit scheme to run in discrete time. This approach eliminates the need for small step sizes and ensures rapid convergence. Unlike existing methods that require specific initial values, our method can provide the network size regardless of the initial values, making it robust to network changes.